1. Field of the Invention
The present invention relates to a method of analyzing a physical property of a golf ball, and more particularly to an analyzing method using a finite element method.
2. Description of the Related Art
A golf ball is hit with a golf club and thus flies. A physical property during hitting such as a resilience characteristic, a launch direction, a spin rate or a hitting feeling greatly influences a subsequent trajectory (a trajectory height or a flight distance). A golf player is very interested in the trajectory (particularly, the flight distance). Therefore, a golf ball manufacturer has aimed at obtaining an improvement in the physical property during hitting and has made an effort toward development.
In the development of the golf ball, first of all, a design is carried out and a trial product is then fabricated. The trial product is subjected to a hitting test and a trajectory is measured together with the physical property during hitting. Data thus obtained by the measurement are decided. If the obtained result is insufficient, the data are fed back to a next design. In the development of the golf ball, thus, the design, the trial production and the hitting test are repeated, which takes a great deal of labor and time.
In place of the hitting test or together with the hitting test, the physical property is measured in the room. Examples of the physical property which can be measured in the room include a resilience coefficient, an amount of compressive deformation (so-called compression), a specific frequency, an impact force and the like. The physical property can be measured more easily in the room than the hitting test. However, the measurement of the physical property in the room is the same as the hitting test in that the trial product is to be fabricated. Thus, it takes a great deal of labor and time to develop the golf ball.
Furthermore, only the data on the physical property of the whole golf ball can be obtained by any of the hitting test and the measurement of the physical property in the room. Accordingly, it is hard to grasp a behavior presented by each portion of the golf ball during impact or compressive deformation. For this reason, trial and error are often repeated from a design to an evaluation in the development of the golf ball.
There has also been proposed a method of carrying out a simulation utilizing a finite element method or the like, thereby evaluating a golf ball without performing trial production. In the finite element method, an analyzing object (a golf ball) is divided into a large number of meshed elements.
However, since the golf ball is a sphere, a complicated operation is required for mesh formation. In particular, it is necessary to devise the mesh formation in order to analyze the golf ball with high precision.
In consideration of such circumstances, it is an object of the present invention to provide a method of analyzing a physical property of a golf ball using a finite element method based on useful mesh formation.
In order to achieve the above-mentioned object, the present invention provides a method of analyzing a physical property of a golf ball comprising the steps of:
(A) dividing, into eight equal portions, the golf ball having a center thereof positioned on an origin of three planes orthogonal to each other at the origin and dividing a xe2x85x9 sphere thus obtained into a large number of meshed elements, thereby obtaining a xe2x85x9 model;
(B) combining the xe2x85x9 model obtained at the step (A), thereby obtaining a finite element golf ball model having an almost spherical shape, an almost semispherical shape or an almost xc2xc spherical shape; and
(C) analyzing the physical property of the golf ball through a finite element method using the finite element golf ball model obtained at the step (B).
The step (A) includes the steps of:
(A1) assuming a small cube in which one apex is coincident with an origin and three of six surfaces are coincident with three planes of the xe2x85x9 sphere, respectively;
(A2) dividing the small cube into meshes, thereby obtaining a nodal point;
(A3) projecting the nodal point included in each of the three surfaces of the small cube which is not coincident with the three planes of the xe2x85x9 sphere onto a spherical surface of a small xe2x85x9 sphere including a small cube and setting an origin to be a center thereof, thereby obtaining a new nodal point;
(A4) dividing as pace between the spherical surface of the small xe2x85x9 sphere and that of the xe2x85x9 sphere through spherical surfaces of a plurality of intermediate xe2x85x9 spheres setting origins to be centers thereof; and
(A5) sequentially repeating an operation for projecting a nodal point present on an inner spherical surface onto a spherical surface adjacent to an outside thereof from the small xe2x85x9 sphere to the xe2x85x9 sphere through the intermediate xe2x85x9 spheres.
In order to achieve the above-mentioned object, another invention provides a method of analyzing a physical property of a golf ball comprising the steps of:
(D) dividing the golf ball into a large number of meshed elements, thereby obtaining a finite element golf ball model having an almost spherical shape; and
(E) analyzing the physical property of the golf ball through a finite element method using the finite element golf ball model obtained at the step (D).
The step (D) includes the steps of:
(D1) assuming a small cube positioned on a center of the golf ball;
(D2) dividing the small cube into meshes, thereby obtaining a nodal point;
(D3) projecting a nodal point on a surface of the small cube onto a spherical surface of a small sphere including a small cube and having a center thereof coincident with a center of the golf ball, thereby obtaining a new nodal point;
(D4) dividing a space between the spherical surface of the small sphere and that of the golf ball through spherical surfaces of a plurality of intermediate spheres having centers thereof coincident with the center of the golf ball; and
(D5) sequentially repeating an operation for projecting a nodal point present on an inner spherical surface onto a spherical surface adjacent to an outside thereof from the small sphere to the spherical surface of the golf ball through the intermediate spheres.
In order to achieve the above-mentioned object, a further invention provides a method of analyzing a physical property of a golf ball comprising the steps of:
(F) dividing the golf ball into a large number of meshed elements, thereby obtaining a finite element golf ball model having an almost spherical shape, an almost semispherical shape or an almost xc2xc spherical shape; and
(G) analyzing the physical property of the golf ball through a finite element method using the finite element golf ball model obtained at the step (F).
The step (F) includes the steps of:
(F1) assuming a semicircle having a diameter almost equal to a diameter of the golf ball;
(F2) assuming a plurality of radial lines extended from a center of the semicircle toward an arc of the semicircle and a plurality of semicircular arcs which are concentric with the semicircle and have smaller diameters than a diameter of the semicircle;
(F3) obtaining a plurality of nodal points coincident with an intersecting point of the semicircle and semicircular arc and the radial line; and
(F4) rotating the semicircle by setting a diameter line thereof to be a rotation axis, thereby expanding the nodal point obtained at the step (F3).
It is preferable that a finite element golf ball model should be obtained through mesh formation such that a ratio of hexahedron elements to all the elements is 95% or more (Step (H)). By a finite element method using the finite element golf ball model, the physical property of the golf ball is analyzed (Step (I)). Consequently, precision in analysis can be enhanced.
A specification suitable for a golf ball can be determined based on the analysis and the golf ball can be manufactured based on the specification.